According to the related art, an apparatus calculates an average magnetic flux density and an average magnetic field in an equivalent element occupied by plural substances including a magnetic material, and analyzes an electromagnetic field produced in a area larger than the equivalent element based on the calculated average magnetic flux density and average magnetic field. A system is also known in which a target area for electromagnetic field analysis is divided into micro-areas, and an H-B curve and a W-B curve each having a ratio α of the minimum magnetic flux density to the maximum magnetic flux density in the micro-areas as a parameter are stored in a data base in order to perform analysis of an electromagnetic field.
In another apparatus according to the related art, the structure of a magnetic domain, which is an area in which the directions of magnetic moments of atoms are oriented in the same direction, in a magnetic material is varied in a stepwise manner. The apparatus calculates the magnetic energy of the magnetic material in each step, and determines the step in which the magnetic energy is minimized. A technology is also known by which micro-magnetization analysis is performed by taking into consideration magnetic properties, such as magnetic anisotropy, in accordance with a program.
Micro-magnetization analysis refers to a technique for modeling a magnetic material, such as a magnetic head of a HDD (Hard Disk Drive), as a collection of small magnets, as illustrated in FIG. 1, in order to simulate the state of magnetic domains numerically. “Micro-magnetization” refers to an individual small magnet or magnetic material element. In micro-magnetization analysis, a mesh of about 10 nm may be used instead of a mesh of a size corresponding to the actual atomic-size order, from the viewpoint of calculation cost. In a typical mesh size (such as 10 nm or less), the magnetization vectors in adjacent mesh areas may form angles of 5° or less, so that the angles may be considered to be substantially continuous.
The motion of micro-magnetization is governed by a governing equation referred to as the LLG (Landau-Lifshitz-Gilbert) equation, as illustrated below:
                                          ∂                          M              →                                            ∂            t                          =                                            -              γ                        ⁢                                                  ⁢                          M              →                        ×                                          H                →                            eff                                +                      α            (                                          M                →                            ×                                                ∂                                      M                    →                                                                    ∂                  t                                                      )                                              (        1        )            where M, γ, α, and Heff are a magnetization vector, a magnetic rotation ratio, a frictional coefficient, and an effective magnetic field, respectively.
The effective magnetic field Heff is a composition of plural magnetic field vectors, as indicated by Equation (2) below. The magnetic fields to which the micro-magnetization is subject include an external magnetic field Hout, a demagnetizing field Hdemag, an anisotropic magnetic field Han, and a magnetic exchange coupling field Hex.{right arrow over (H)}eff={right arrow over (H)}out+{right arrow over (H)}demag+{right arrow over (H)}an+{right arrow over (H)}ex  (2)
The magnetic exchange coupling field Hex exerts a force that originally acts between adjacent atoms. In order to perform micro-magnetization analysis by using an analysis model in which the size of the mesh is larger than the inter-atomic distance while maintaining calculation accuracy, an analysis model may be adopted in which the size of the mesh is so small (such as 10 nm or less) that the angles of adjacent magnetization vectors vary by 10 degrees or less.
Micro-magnetization analysis has been mainly used for small amounts of magnetic material of micron order as an analysis target. However, due to advances in computing technology, it is now possible to apply micro-magnetization analysis for magnetic materials of several dozen micron order. It is expected that magnetic material areas of even greater sizes, such as those of motors and transformers, will be selected as analysis targets.
Patent Document 1: Japanese Laid-open Patent Publication No. 2005-43340
Patent Document 2: Japanese Laid-open Patent Publication No. 2004-347482
Patent Document 3: Japanese Laid-open Patent Publication No. 2004-219178
Patent Document 4: Japanese Laid-open Patent Publication No. 2005-100067
Thus, the mesh size may preferably be 10 nm or less in order to enable highly accurate micro-magnetization analysis. As the size of the analysis target area is increased, the number of meshes (which may be hereafter referred to as the number of mesh areas) that need to be handled increases. An increase in mesh size decreases the degrees of freedom required for calculation, so that calculation time can be reduced. However, when the mesh size is increased, the adjacent magnetization vectors may form an angle of more than 10°. Thus, simply increasing the mesh size may result in a decrease in calculation accuracy.
Further, in a micro-magnetization analysis according to related art, an increase in mesh size (such as more than 10 nm) results in an increase in the rotation angle of the magnetization vectors (angle formed by adjacent magnetization vectors), thus preventing accurate micro-magnetization analysis. Specifically, the accuracy of calculation of the magnetic exchange coupling energy or the magnetic exchange coupling field may be lowered.
The object and advantages of the disclosure will be realized and attained by means of the elements and combinations particularly pointed out in the claims.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the invention, as claimed.